automata 5 Sections AutomataTheory Doc

Def MinAuto(Auto) == A(l.Auto(l))

Thm* Auto:Automata(Alph;St), S:Type, A:Automata(Alph;S). Fin(Alph) Fin(S) Con(A) (S ~ (x,y:Alph*//(x LangOf(Auto)-induced Equiv y))) LangOf(Auto) = LangOf(A) A MinAuto(Auto) any_iso_min_auto

Thm* Auto:Automata(Alph;St). Fin(Alph) & Fin(St) Con(MinAuto(Auto)) min_auto_con

Thm* Auto:Automata(Alph;St), l:Alph*. (Result(MinAuto(Auto))l) = l x,y:Alph*//(x LangOf(Auto)-induced Equiv y) min_auto_comp

Thm* Auto:Automata(Alph;St). LangOf(Auto) = LangOf(MinAuto(Auto)) min_auto_sound